A. WHY ARE DIFFERENT MATERIALS DIFFERENT?

Different substances have different properties because

• They contain different elements and different combinations of elements.
  
• They contain different types of chemical bonds.
  
• There are different sizes of the molecular units.
  
• Similar units within the solid-state structure may be assembled in different ways—the molecular packing arrangements may be different, or the geometry of linkage in an extended structure may vary.

These and several other factors are considered in the following sections.

B. THE ROLE OF DIFFERENT ELEMENTS

Certain elements in the periodic table play a larger role in materials science than do others. This brings about a significant simplification in the chemistry. Although most of the elements in the periodic table are used in one way or another in materials science, the 20 or so elements emphasized in Figure 2.1 are used in a disproportionate number of useful materials. These include nonmetals such as carbon, silicon, boron, nitrogen, oxygen, and phosphorus, and metals such as aluminum, magnesium, titanium, tin, iron, copper, chromium, and nickel. Other elements such as arsenic, cadmium, gallium, thallium, germanium, platinum, silver, and gold are also employed, but often in smaller quantities and for specialized uses.

Figure 2.1. Periodic table showing elements (in boldface) that play a major role in materials science.

The influence of different elements on properties is well known for small molecules, but in the science of solids it is particularly crucial. For example, although carbon and silicon are both in group IVA (14) of the periodic table and have many chemical similarities, the replacement of carbon by silicon in polymers, in the diamond structure, or in ceramics, brings about far-reaching changes to the properties. These differences result from the different sizes of the atoms, their electronic configuration, the ease with which the outer electrons can be lost, and the types and lengths of the bonds they form with neighboring atoms. For example, silicon has the same outer-shell electron configuration as carbon, but it is larger and forms longer covalent bonds to its neighbors. Moreover, unlike carbon, it is reluctant to form double bonds to oxygen, nitrogen, or other silicon atoms. Silicon also has the ability to expand its octet and form bonds to four, five, or six other atoms, whereas carbon is restricted to bonds to two, three, or four other atoms. Several of these differences are responsible for the fact that pure silicon (with the same extended solid-state structure as diamond) is a semiconductor whereas diamond is not. When both are doped with “impurities,” silicon is a much better semiconductor than diamond.

The size of atoms increases down a group in the periodic table because additional electron shells have been added. However, atomic radii decrease in going from left to right across the periodic table because of the rising number of positive charges in the nucleus and their increased pull on the outer electrons. The ionization potential (the energy required to remove an electron from an isolated atom) decreases down a group but increases from left to right.

Thus, if we compare elements that are in different groups in the periodic table, or are in the same group but are not adjacent to each other, then the differences become profound. Some similarities exist between silicon and germanium, but far fewer between silicon and tin or lead. The introduction of transition metals changes the picture even more profoundly because of the ability of these elements to utilize their d orbitals, generate colored materials, enhance electrical conductivity, and provide highly reflective surfaces. Indeed, one of the most important consequences of the replacement of one element by another is the change this brings about to the chemical bonding.

C. DIFFERENT TYPES OF CHEMICAL BONDS

Theories of chemical bonding range from the purely descriptive, which are useful for visualization, to complex calculations based on quantum interpretations and approximations to the Schrödinger equation. In this book we will utilize the more descriptive approach. In the simplest interpretation of molecular and materials structure there are five types of forces that hold the components of solids together—van der Waals associations, covalent bonds, coordinate bonds, ionic assemblies, and metallic structures. These differ greatly in strength, with van der Waals forces being the weakest. The characteristics of materials with different bond types are shown in Table 2.1.

TABLE 2.1. Types of Bonds Found in Solids

1. Van der Waals Forces and the Lennard-Jones Potential

Van der Waals forces are the weak interactions that hold neutral molecules together in the solid state. The attractions arise from the “exchange forces” between electrons in the outer regions of the interacting molecules. Van der Waals forces are responsible for the assembly of covalent molecules into crystal lattices, and the combination of attractions and molecular shape-fitting are responsible for the different packing patterns that arise in nonionic crystals. Because van der Waals forces are weak they are easily disrupted by heat, which explains why solids consisting of closely packed small molecules tend to melt at low or moderate temperatures.

In practice, the distance between atoms or groups of atoms can be defined by terms such as the Lennard-Jones potential, given in equation 1, where V is the potential energy, r is the distance between the interacting atoms, and ε is the depth of the well that corresponds to the equilibrium distance between the atoms:

Figure 2.2. Potential energy–atom separation curves for separate attractive and repulsive terms in the Lennard-Jones equation, and the combined interaction energies, showing how the attractions increase with decreasing separation but are counteracted by the nuclear–nuclear repulsions at short distances. The minimum in the curve represents the distance at which these two forces balance each other. The energy decrease is the force that holds covalent molecules together in a crystalline lattice, and is the driving force for shape-fitting by the molecules to allow the most efficient minimization of the overall energy. Note that the general shape of the van der Waals curve can also be used to explain the preferred conformation of a molecule caused by the attractions or repulsions of the groups connected to a rotatable bond.

(1)

Figure 2.2 shows how these forces arise by a balancing of the long-range non-bonding attractions (the 10⁶ term) between atoms and molecules against the repulsions (the 10¹² term) that result from too close an approach of the positively charged atomic nuclei.

2. Covalent Bonds

Covalent bonds are much stronger than van der Waals interactions, and considerable energy is needed to break them. For example, a Si—Si bond has an energy of 52 kcal/mol, an aliphatic carbon–carbon bond has a value of 83 kcal/mol, and a CN bond has an energy as high as 213 kcal/mol. Covalent bonds arise between participating atoms through the pairing of outer-level electrons with opposite spin (Figure 2.3). One electron is provided by each participating atom. The electrons are located in orbitals, the overlap of which yields a spin-paired bond. When more than two electrons contribute to a bond (double, triple, or quadruple bonds) the bonds become shorter and stronger. Thus, the CC bond has an energy of 146 kcal/mol, CO has a value of 177–179 kcal/mol, and PO has a value of 110 kcal/mol. Some of the highest covalent bond energies are found for bonds, such as CN or PO, which have a high polarity (see later).

Figure 2.3. Covalent bonding as represented by (a) the electron dot model and (b) the orbital overlap concept. Coordinate bonding, in which one atom supplies both of the electrons for the bond, is depicted in rows (c) and (d).

a. Bond Angles.

The overall shape of a molecule can be traced to its bond angles and molecular conformation. Three factors control the bond angles in an isolated small molecule—the inherent orientation of molecular orbitals, the repulsion of the electron pairs in nearby bonds, and the attractions or repulsions of groups of atoms that are linked to the central atom.

In the simplest sense the bond angles in an isolated molecule can be understood in terms of the angles between orbitals, as illustrated in Figure 2.4. Thus, in principle, a central atom with three unpaired electrons in three p orbitals that are oriented 90° from each other (orthogonal) will overlap the orbitals of three other atoms to give a pyramidal molecule with approximately 90° bond angles. Some representative bond angles are given in Table 2.2, and it is clear that these angles cannot be explained exclusively by the inherent orientation of simple molecular orbitals. For example, if the simple orientation of p orbitals were involved, all the H–N–H bond angles in ammonia would be 90°, and the H–O– H angle in water would also be 90°, and these are not the angles found by experiment.

Figure 2.4. Orientation of nonhybridized orbitals. Mixing of these generates hybrid orbitals with different bond angles, as illustrated in Figure 2.5.

In practice, the p orbitals combine with a spherical s orbital or with d orbitals to form hybrid orbitals that give rise to different bond angles. Thus, one p orbital hybridized with an s orbital gives an sp hybrid and a bond angle of 180°. The sp² hybrids give planar molecules with 120° bond angles, and some elements can form hybrid orbital arrangements by mixing in s orbital character to connect to four other atoms, in which case the resultant sp³ hybrid orbitals of the central element will generate a set of 109.5° bond angles. Thus, four bonds to a central element yield a tetrahedral structure. This is the situation found in many carbon and silicon compounds and in the extended lattices of diamond and silicon. The existence of sp³d hybrids explains the combination of 90° and 120° angles (trigonal bipyramid) when five bonds radiate from a central atom, and an sp³d² arrangement is consistent with all the angles being 90° (octahedral) with six bonds radiating from the central element (Figure 2.5). Thus, the underlying supposition in this approach is that inherent orbital structure and hybridization control the bond angles and, thereby, the shape of a molecule.

TABLE 2.2. Experimentally Determined Bond Angles^a

^aSymbols key: indicates a lone pair of electrons, :: indicates two lone pairs; tet = tetrahedral, ps-tet = pseudotetrahedral, tbp = trigonal bipyramidal, oct = octahedral, sq-pl = square planar, tpl = trigonal planar.
^bNote that bond angles in a solid-state structure may be distorted from “molecular” values by crystal-packing forces.
^cNote also that bond angles are meaningful only for covalent or coordinate bonding systems and not for ionic crystals.

What controls the hybridization? One factor is the mutual repulsion of the electron pairs that constitute each bond. This is known as the valence shell electron pair repulsion (VSEPR) concept. The basis of this approach is that electron pairs attempt to move as far away from each other as possible. Depending on the number of bonds around a central atom, these repulsions will generate specific structures with specific bond angles. Thus, two electron pairs (two bonds) will widen the bond angle to 180°. Three electron pairs will yield a trigonal planar (120°) structure. Four electron pairs yield a tetrahedral structure, five will give rise to a trigonal bipyramid, and six will yield an octahedral arrangement. Moreover, if unbonded electrons are left over in “lone-pair orbitals,” these, too, will repel nearby bonds and help to determine the molecular shape. For example, ammonia is pyramidal rather than trigonal planar because there is a fourth orbital—the lone pair on the nitrogen. Thus, the approximately 109° H–N–H angles in ammonia reflect the presence of the nonbonding lone pair, which induces a pseudotetrahedral structure (i.e., tetrahedral if the lone pair is included). In water there are two lone-pair orbitals and a pseudotetrahedral arrangement of bonds, with H–O–H angles near 109.5°. A linear bond arrangement could be the result of two large atoms or groups linked to a connecting atom to get as far away from each other as possible. Three atoms linked to a central atom can minimize their repulsions by forming a trigonal planar unit. Four atoms around a central atom require a tetrahedral structure to minimize their mutual repulsions. Five and six atoms form a trigonal bipyramidal and octahedral arrangements, respectively. Oxygen atoms in water have two lone-pair orbitals, which force the H–O–H angle to approximate to 109.5°. The same is true of the oxygens in neutral silicates or silicone polymers, and this narrows the Si—O–Si angle considerably below what might otherwise have been predicted to be 180°. In practice, the Si—O–Si bond angle is extremely variable because oxygen can readily use different hybrid orbitals in response to solid-state packing forces or physical stress. So, bond angles and molecular shapes can be understood either in terms of the orbital configurations or in terms of atomic repulsions. Although it can be argued that the inherent orientation of hybrid orbitals or VSEPR predominate, the answer probably lies in a balance of the two. Whether electron pair repulsion induces orbital hybridization or vice versa is a moot question. They have the same effect, and they work in concert.

Figure 2.5. Bond angles and geometries imposed by different hybrid orbital arrangements.

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